View source for Strategic voting

{{Short description|Choosing a candidate other than preferred to undercut a less desired one}}
{{Use dmy dates|date=May 2020}}
{{voting}}
'''Strategic''' or '''tactical voting''' is voting in consideration of possible ballots cast by other voters in order to maximize one's satisfaction with the election's results.<ref>{{cite book |last=Farquharson |first=Robin |url=https://books.google.com/books?id=fIMHAQAAMAAJ |title=Theory of Voting |publisher=Blackwell (Yale U.P., U.S.) |year=1969 |isbn=978-0-631-12460-3}}</ref> 

[[Gibbard's theorem]] shows that no voting system has a single "always-best" strategy, i.e. one that always maximizes a voter's satisfaction with the result, regardless of other voters' ballots. This implies all voting systems can sometimes encourage voters to strategize. However, weaker guarantees can be shown under stronger conditions. Examples include [[Single-peaked preferences|one-dimensional preferences]] (where the [[Median voting rule|median rule]] is strategyproof) and [[dichotomous preferences]] (where [[approval voting|approval]] or [[score voting]] are strategyproof).

With large electoral districts, [[Electoral list|party list]] methods tend to be difficult to manipulate in the absence of an [[electoral threshold]]. However, biased [[Apportionment (politics)|apportionment methods]] can create opportunities for strategic voting, as can small electoral districts (e.g. those used most often with the [[single transferable vote]]). Proportional representation systems with small districts often involve large-scale [[vote management]] operations, which are common in countries using [[Single transferable vote|STV-PR]] such as [[Republic of Ireland|Ireland]].

== Common types of strategic voting ==
{{More citations needed section|date=April 2024}}
Some types of strategic voting described in the literature are:

; {{visible anchor|Compromising}}, includes [[Favorite betrayal criterion|''favorite betrayal'']].<ref name="Armytage-SVN">{{cite journal | last=Green-Armytage | first=James | title=Strategic voting and nomination | journal=Social Choice and Welfare | volume=42 | issue=1 | date=2014 | issn=0176-1714 | doi=10.1007/s00355-013-0725-3 | pages=111–138| url=https://mpra.ub.uni-muenchen.de/32200/1/MPRA_paper_32200.pdf }}</ref>{{rp|117}}
{{See also|Lesser-evil voting}}
: A voter ranks or rates a candidate they dislike – a "lesser evil" – higher in the hope of getting them elected, thus preventing an even worse candidate from being elected.
: This type of strategic voting includes the [[First-past-the-post election system|first-past-the-post]] strategy of voting for the [[Lesser of two evils principle#In modern elections|lesser of two evils]], as well as the more general [[Favorite betrayal criterion|''favorite betrayal'']] strategy. A sufficiently strong compromising incentive, possibly strengthened by a [[strategic nomination|strategic exit]] incentive,<ref name="Armytage-SVN" />{{rp|118}} can lead to or reinforce two-party rule as voters will abandon minor-party candidates to support stronger major-party candidates. This effect is called [[Duverger's law]].<ref name=":12">{{Cite book |last=Volić |first=Ismar |url=http://dx.doi.org/10.2307/jj.7492228 |title=Making Democracy Count |year=2024 |publisher=Princeton University Press |isbn=978-0-691-24882-0 |chapter=2: Duverger's law |doi=10.2307/jj.7492228}}</ref>
: While methods that pass the [[sincere favorite criterion]] never incentivize a voter to rank or rate a lesser evil above one's favorite, they may still incentivize voters to rank or rate the lesser evil ''higher''. For instance, in [[approval voting]], a voter may have an incentive to strategically approve a lesser evil that they dislike. Although not considered favorite betrayal, this is also a type of compromise strategy.
: ''Most affects:'' [[Instant-runoff voting|instant-runoff]] (RCV), [[two-round system]], and (especially strong for) [[Plurality voting|plurality]].<ref name="Hodge Klima 2018 p. 922">{{cite book |last1=Hodge |first1=J.K. |title=The Mathematics of Voting and Elections: A Hands-On Approach |last2=Klima |first2=R.E. |publisher=American Mathematical Society |year=2018 |isbn=978-1-4704-4287-3 |series=Mathematical World |chapter=6}}</ref>
: ''Also affected:'' [[Borda count|Borda]], [[Score voting|Score]], [[approval voting]].<ref name="Armytage-SVN" />{{rp|at=prop. 4, note}}
: ''Immune:'' [[Coombs' method]],<ref name="Armytage-SVN"/>{{rp|at=prop. 4, note}} [[Anti-plurality voting|antiplurality]].

; {{visible anchor|Burial|Burying}}
: A voter ranks or rates a candidate lower in the hope of defeating them. For example, a voter may insincerely rank or rate a perceived strong candidate last in order to help their preferred candidate win.<ref name="Armytage-SVN" />
: Game theory arguments suggest that if burial incentive is sufficiently severe, a method may induce a race to the bottom. Each voter follows a strategy that, in isolation, helps their candidate win, but the result is that a candidate that nobody likes gets elected instead.<ref name="Monroe">{{Cite conference |last=Monroe |first=Burt |date=September 2001 |title=Raising Turkeys: An Extension and Devastating Application of Myerson-Weber Voting Equilibrium |url=https://www.accuratedemocracy.com/archive/condorcet/Monroe/004004MonroeBurt.pdf |conference=American Political Science Association}}</ref>
: ''Most affects:'' [[Borda count|Borda]], [[Anti-plurality voting|antiplurality]], [[approval voting]], and [[Score voting|Score]].<ref name="Armytage-SVN" />
: ''Also affected:'' Most [[Condorcet method]]s, with the exception of IRV-Condorcet hybrids.<ref name="Monroe" /><ref name="Armytage-Hare">{{cite journal | last=Green-Armytage | first=James | title=Four Condorcet-Hare hybrid methods for single-winner elections. | journal=Voting Matters | volume=29 | issue=1 | date=2011 | url=http://www.mcdougall.org.uk/voting-matters/ISSUE29/I29P1.pdf}}</ref><ref name="h794">{{cite journal | last=Green-Armytage | first=James | title=A Dodgson-Hare synthesis | journal=Constitutional Political Economy | volume=34 | issue=3 | date=2023 | issn=1043-4062 | doi=10.1007/s10602-023-09392-2 | pages=458–470}}</ref>
: ''Immune:'' [[Instant-runoff voting]] and [[plurality voting]].

; {{visible anchor|Turkey-raising|Pushover|Raiding|Pied-piper}} (sometimes called ''pushover'' or ''pied-piper.'' Includes ''[[Party raiding|raiding]]''.)
: A voter gives a high rank to a weak (i.e. ''pushover'') candidate, but not with the intent of getting them elected. Instead, the voter intends for the weak candidate to eliminate a strong alternative, who would otherwise keep the voter's preferred candidate from winning.<ref>{{cite web |author=Matthew S. Cook |date=March 2011 |title=Voting with Bidirectional Elimination |url=http://economics.stanford.edu/files/Matthew%20Cook%20Honors%20Thesis.pdf |url-status=dead |archive-url=https://web.archive.org/web/20111120014436/http://economics.stanford.edu/files/Matthew%20Cook%20Honors%20Thesis.pdf |archive-date=20 November 2011 |access-date=21 April 2012 |publisher=Voting with Bidirectional Elimination}}</ref> [[Party Raiding|Party raiding]] is a well-known example of such a strategy.<ref name="alvar99b2">{{cite web |author=R. Michael Alvarez |author2=Jonathan Nagler |date=1999 |title=Analysis of Crossover and Strategic Voting |url=http://polmeth.wustl.edu/media/Paper/alvar99b.pdf |url-status=dead |archiveurl=https://web.archive.org/web/20100625234325/http://polmeth.wustl.edu/media/Paper/alvar99b.pdf |archivedate=25 June 2010 |accessdate=21 April 2014 |publisher=Society for Political Methodology (American Political Science Association; Washington University in St. Louis)}}</ref><ref>Negrin, Matt. "[https://abcnews.go.com/Politics/OTUS/democrats-decide-winner-michigan/story?id=15809682 Could Democrats Decide the Winner in Michigan?]" ''ABC News,'' 28 Feb. 2012. Retrieved 9 Dec. 2017.</ref>
: ''Most affects:'' Multi-round rules like [[Instant-runoff voting|instant-runoff]], [[Two-round system|two-round]], and [[Partisan primary|primary elections]].
: ''Immune:'' [[Plurality voting|Plurality]] and all commonly-used [[rated voting]] systems, including [[score voting]] and [[approval voting]].
; {{visible anchor|Compression|Bullet voting|Truncation|Exaggeration}} (sometimes called ''leveling''. Includes ''[[bullet voting]]'' and ''truncation.'')
: Compression is a strategy where a voter refuses to disclose which of two candidates they honestly prefer (i.e. both candidates are given the same rating or ranking). Compression is unique in that it does not involve a rank reversal: in compression, a voter who prefers A to B doesn't claim to prefer B to A, only that they're indifferent between them.
: Like ''compromising'' and ''burial'', the strategy involves [[Exaggeration|exaggerating]] differences between candidates: ranking or rating lesser evils equal to one's favorite is similar to compromising, and ranking or rating okay candidates equal to one's most loathed candidate is similar to burial. The latter is also called ''truncation''.
: Compression has the advantage of making it less likely for a disliked candidate to win, but the disadvantage that it reduces the chances of the best candidate winning.
: ''Most affects'': [[Rated voting]].<ref name="Nagel">{{Cite journal |last=Nagel |first=Jack H. |date=February 2007 |title=The Burr Dilemma in Approval Voting |url=https://www.jstor.org/stable/10.1111/j.1468-2508.2007.00493.x |journal=[[The Journal of Politics]] |volume=69 |issue=1 |pages=43–58 |doi=10.1111/j.1468-2508.2007.00493.x |jstor=10.1111/j.1468-2508.2007.00493.x  |quote=Therefore, strategic approval voting consists primarily of truncation and expansion of the approved list...}}</ref>
: ''Immune:'' [[Random ballot]] and methods that require strict rankings.

==Frequency and susceptibility==

Strategic voting is highly dependent on the voting method being used. A strategic vote which improves a voter's satisfaction under one method could have no effect or be outright self-defeating under another method. [[Gibbard's theorem]] shows that no deterministic single-winner voting method can be completely immune to strategy, but makes no claims about the severity of strategy or how often strategy succeeds.

Later results show that some methods are more manipulable than others.<ref name="Armytage-SVN" /><ref name="Durand MCN">{{cite arXiv |last1=Durand |first1=François |title=On the Manipulability of Voting Systems: Application to Multi-Carrier Networks |date=2012-04-29 |eprint=1204.6455 |class=cs.NI |last2=Mathieu |first2=Fabien |last3=Noirie |first3=Ludovic}}</ref>

[[Michel Balinski]] and Rida Laraki, the inventors of the [[majority judgment]] method, performed an initial investigation of this question using a set of [[Monte Carlo method|Monte Carlo]] simulated elections based on the results from a poll of the [[2007 French presidential election]] which they had carried out using rated ballots. Comparing [[range voting]], [[Borda count]], [[plurality voting]], [[approval voting]] with two different absolute approval thresholds, [[Condorcet voting]], and [[majority judgment]], they found that range voting had the highest (worst) strategic vulnerability, while their own method majority judgment had the lowest (best).<ref name="auto2">{{cite book |last1=Balinski |first1=Michel |title=In Situ and Laboratory Experiments on Electoral Law Reform |last2=Laraki |first2=Rida |year=2011 |isbn=978-1-4419-7538-6 |series=Studies in Public Choice |volume=25 |pages=13–54 |chapter=Election by Majority Judgment: Experimental Evidence |doi=10.1007/978-1-4419-7539-3_2}}</ref> Further investigation would be needed to be sure that this result remained true with different sets of candidates. 

[[Electoral list|Party-list proportional]] methods typically show less strategic voting,<ref>{{cite journal |last1=Shikano |first1=Susumu |last2=Herrmann |first2=Michael |last3=Thurner |first3=Paul W. |year=2009 |title=Strategic Voting under Proportional Representation: Threshold Insurance in German Elections |url=https://doi.org/10.1080/01402380902779147 |journal=West European Politics |volume=32 |issue=3 |pages=634–656 |doi=10.1080/01402380902779147 |s2cid=154800908}}</ref> although the existence of electoral thresholds can lead voters to vote strategically to avoid [[Wasted vote|wasted votes]].<ref name="v742">{{cite journal | last=Jenssen | first=Anders Todal | title=Tactical Voting in Norway: Context, Motives and Occurrence | journal=Scandinavian Political Studies | volume=39 | issue=1 | date=2016 | issn=0080-6757 | doi=10.1111/1467-9477.12057 | pages=22–51 |quote=Of the voters in the survey, 18.3 percent reported casting a tactically motivated vote. The 4 percent threshold on the distribution of compensatory seats, the competition for the last district seats and the composition of government coalitions triggered tactical voting.}}</ref>

==Mitigation==
Switching from a method that is highly manipulable to one that is more resistant would help discourage widespread strategic voting, all else equal.

From a voting method, it's possible to design another voting method that attempts to strategize on behalf of the voter. Such methods are called ''declared strategy voting'' methods, and seek to improve a method's strategy resistance by moving the strategy into the method itself. DSV methods have been proposed for [[plurality voting]], [[approval voting]], and [[score voting]].<ref name="Cranor">{{Cite thesis |last=Cranor |first=Lorrie Faith |title=Declared-strategy voting: an instrument for group decision-making |date=1996 |degree=PhD |publisher=Washington University |url=https://lorrie.cranor.org/pubs/diss/ |place=USA}}</ref><ref name="RLDSV1">{{Cite thesis |last=Legrand |first=Robert Hampton |title=Computational aspects of approval voting and declared-strategy voting |date=2008 |degree=PhD |publisher=Washington University |url=https://dl.acm.org/doi/abs/10.5555/1467782 |place=USA}}</ref><ref name="RLDSV2">{{Cite conference |last1=Legrand |first1=Robert Hampton |last2=Cytron |first2=Ron K. |title=Approval-rating systems that never reward insincerity |conference=COMSOC-2008: 2nd International Workshop on Computational Social Choice |conference-url=https://comsoc-community.org/proceedings/2008/ |url=https://comsoc-community.org/assets/proceedings/comsoc-2008/LeGrand.pdf |year=2008}}</ref>

==Coordination==
{{Unreferenced section|date=August 2024}}
The nature of strategic voting requires some level of coordination. Because it is a system of voting that assesses outcomes before casting one's vote, coordination towards the outcome is a prerequisite for strategic voting. There must be some kind of coordination device in order to vote strategically. Coordination devices, though not the only device, are typically opinion polls. For example, if there was  two similarly appealing majority candidates and a minority candidate and voters were given the choice between the three, polls are imperative to coordinating votes for either majority candidate.<ref>{{Cite journal |last1=Andonie |first1=Costel |last2=Kuzmics |first2=Christoph |date=2012-11-01 |title=Pre-election polls as strategic coordination devices |url=https://linkinghub.elsevier.com/retrieve/pii/S0167268112001813 |journal=Journal of Economic Behavior & Organization |volume=84 |issue=2 |pages=681–700 |doi=10.1016/j.jebo.2012.09.014 |issn=0167-2681}}</ref> Polls are then a tool used by voters to ensure that the minority candidate doesn't obtain office, which would be adverse to Duverger's law.  

Tactical voting may occur in isolation or as part of an organized campaign. In the former situation, electors make their own judgement as to the most effective way to (typically) prevent the election of a specific candidate or party. In the latter, one or more parties or groups encourage their supporters to vote tactically in an effort to influence the outcome. 

The form that coordinated tactical voting takes depends largely on the electoral system of the polity. For example, vote thresholds in a proportional representation electoral system are found to prompt voters to coordinate their votes.<ref>{{Cite journal |last1=Blais |first1=André |last2=Erisen |first2=Cengiz |last3=Rheault |first3=Ludovic |date=June 2014 |title=Strategic Voting and Coordination Problems in Proportional Systems: An Experimental Study |url=https://journals.sagepub.com/doi/10.1177/1065912913520573 |journal=Political Research Quarterly |language=en |volume=67 |issue=2 |pages=386–397 |doi=10.1177/1065912913520573 |issn=1065-9129}}</ref> For example, in the 2018 Swedish election, thresholds led voters who identified with a small party to consider the outcomes of their votes on the system of government as well as the other parties' outcomes.<ref>{{Cite journal |last=Fredén |first=Annika |title=Threshold Insurance Voting in PR Systems: A Study of Voters' Strategic Behavior in the 2010 Swedish General Election |journal=Journal of Elections, Public Opinion and Parties |date=2014-10-02 |volume=24 |issue=4 |pages=473–492 |url=https://www.tandfonline.com/doi/abs/10.1080/17457289.2013.872118 |doi=10.1080/17457289.2013.872118 |issn=1745-7289}}</ref> The voting history of the polity also influences coordination efforts: in proportional representation systems with little voting history, voters tend to vote more sincerely than engage in strategic voting due to the unknown nature of what party will be most viable.<ref>{{Cite journal |last1=Blais |first1=André |last2=Erisen |first2=Cengiz |last3=Rheault |first3=Ludovic |date=June 2014 |title=Strategic Voting and Coordination Problems in Proportional Systems: An Experimental Study |url=https://journals.sagepub.com/doi/10.1177/1065912913520573 |journal=Political Research Quarterly |language=en |volume=67 |issue=2 |pages=386–397 |doi=10.1177/1065912913520573 |issn=1065-9129}}</ref> 

Organized tactical voting in which a political party mounts a campaign calling on its supporters not to vote for their own favored candidates, but for those of a party which it perceives as more likely to defeat a common opponent, is less common. An example is the [[1906 United Kingdom general election]], where the [[Liberal Party (UK)|Liberals]] (incidentally, the predecessors of the Liberal Democrats from the previous example) and the then-insurgent [[Labour Party (UK)|Labour Party]] (founded in 1900) agreed on the [[Gladstone-MacDonald pact]], under which certain Liberal candidates would stand aside in favor of Labour ones, again to ensure that the Conservative candidates would not win on the basis of a split anti-Tory vote.

An intermediate case also exists, where a non-party campaign attempts to coordinate tactical voting, typically with the goal of defeating a certain party. Cases of this include the Canadian [[Anything But Conservative]] campaign, which opposed the [[Conservative Party of Canada]] in the [[2008 Canadian federal election|2008]] and [[2015 Canadian federal election|2015 federal elections]], or the [[Smart Voting]] campaign organized by Russia's [[Anti-Corruption Foundation]] with the goal of opposing and weakening the [[United Russia]] party in the [[2021 Russian legislative election]]. This also occurred in the UK 2019 General Election, where voting groups such as Tactical Vote and Turf Out The Tories, promoted tactical voting to prevent a Conservative majority.<ref>{{Cite journal |last=Hughes |first=Niall |date=2020 |title=Strategic Voting in Two-Party Legislative Elections |url=https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3590197 |journal=SSRN Electronic Journal |doi=10.2139/ssrn.3590197 |ssrn=3590197 |issn=1556-5068}}</ref>

== Examples in real elections ==
=== Canada ===
The observed effect of [[Duverger's law]] in Canada is weaker than in other countries.<ref name="Duverger2">Duverger's Law of Plurality Voting The Logic of Party Competition in Canada, India, the United Kingdom and the United States, 2009, André Blais, Bernard Grofman, Shaun Bowler</ref> In the [[1999 Ontario general election|1999 Ontario provincial election]], strategic voting was encouraged by opponents of the [[Ontario Progressive Conservative Party|Progressive Conservative]] government of [[Mike Harris]]. This failed to unseat Harris but succeeded in suppressing the [[Ontario New Democratic Party]] vote to a historic low.

In the [[2004 Canadian federal election|2004 federal election]], and to a lesser extent in the [[2006 Canadian federal election|2006 election]], strategic voting was a concern for the federal [[New Democratic Party]] (NDP). In the 2004 election, the governing Liberal Party was able to convince many New Democratic voters to vote Liberal to avoid a Conservative government.{{citation needed|date=January 2013}} In the 2006 elections, the Liberal Party attempted the same strategy, with Prime Minister [[Paul Martin]] asking New Democrats and Greens to vote for the Liberal Party to prevent a Conservative win. The New Democratic Party leader [[Jack Layton]] responded by asking voters to "lend" their votes to his party, suggesting that the Liberal Party was bound to lose the election regardless of strategic voting.{{Cn|date=May 2024}} This failed to prevent the Conservatives from winning the election, although they did not win a majority of seats.{{Cn|date=May 2024}}

During the [[2015 Canadian federal election|2015 federal election]], strategic voting was used extensively against the [[Conservative Party of Canada|Conservative]] government of [[Stephen Harper]], which had benefited from [[vote splitting]] among centrist and left-leaning parties in the [[2011 Canadian federal election|2011 election]].<ref>{{cite web |date=18 October 2015 |title=Strategic Voting Must Include Casting Your Ballot for the Green Party |url=http://www.huffingtonpost.ca/ken-wu/strategetic-voting-green_b_8305938.html |newspaper=The Huffington Post}}</ref><ref>{{cite AV media |url=http://www.cbc.ca/radio/thecurrent/the-current-for-october-15-2015-1.3271954/federal-election-2015-strategic-voters-challenge-democracy-1.3271971 |title=Federal Election 2015: Strategic voters challenge democracy |date=15 October 2015 |medium=Radio broadcast |publisher=[[CBC Radio]] |first1=Anna Maria |last1=Tremonti}}</ref> Following the landslide victory of the [[Liberal Party of Canada|Liberals]] led by [[Justin Trudeau]] over Harper's Conservatives, experts argued that this dramatic increase in support for the Liberals at the expense of the NDP and [[Green Party of Canada|Green Party]] was partially due to strategic voting for Liberal candidates.<ref>{{cite news |last1=Press |first1=Jordan |date=20 October 2015 |title=Canada Election Result Numbers Show Canadians Voted Strategically: Experts |newspaper=Huffington Post |url=http://www.huffingtonpost.ca/2015/10/20/canada-election-results-strategic-voting_n_8343104.html}}</ref> In three weeks, 1.4 million voters switched from NDP to Liberal. In at least two closely-contested ridings, strategic voting websites obtained enough pledges to account for the victory margin of the Liberal candidate.<ref>{{cite news |first1=Ali |last1=Kashani |title=Proof That Trudeau Won Because Strategic Voting Works |date=22 October 2015 |url=http://www.huffingtonpost.ca/ali-kashani/strategic-voting-justin-trudeau_b_8351796.html}}</ref>

=== France ===
The [[two-round system]] in France shows strategic voting in the first round, due to considerations which candidate will reach the second round.<ref>[https://montreal.ctvnews.ca/france-s-election-strategic-voting-among-montreal-s-french-citizens-1.5855627 France's election: 'strategic' voting among Montreal's French citizens, CTV News]</ref>
[[File:Anti-Macron_stencil_2.jpg|right|thumb|Stenciling on a Parisian sidewalk ahead of the first round of the [[2017 French presidential election]] invoking "{{Lang|fr|votez utile}}" (strategic voting) as a reason for voters to vote for [[François Fillon]] instead of [[Emmanuel Macron]]]]

=== Germany ===
The [[mixed-member proportional representation]] allows to estimate the share of strategic voters in [[first-past-the-post voting]] due to the separate votes for party-lists and local single-winner electoral district candidates. The vote for party-lists is considered sincere if the party vote share is significantly above the 5% electoral threshold in Germany. In Germany the share of strategic voters was found around 30%, which decreased to 9% if only non-allied party candidates were contenders for the electoral district winner.<ref>[https://www.bu.edu/econ/files/2013/03/May-4-Spenkuch.pdf On the Extent of Strategic Voting, Jorg L. Spenkuch, 2012]</ref> In a contentious election year the share of strategic voters increased to around 45%.

Due to electoral threshold in [[party-list proportional representation]] one party asked in several elections their voters to vote for another allied party to help this party cross the electoral threshold.<ref>[https://www.zeit.de/politik/deutschland/2013-09/FDP-Leihstimme-Bundestagswahl-CDU Als die CDU noch Leihstimmen zu vergeben hatte, Christopher Pramstaller, 2013 (German)]</ref>

=== Hong Kong ===
In [[Hong Kong]], with its [[party-list proportional representation]] using [[largest remainder method]] with the [[Hare quota]], voters supporting candidates of the [[pro-democracy camp]] often organize to divide their votes across different tickets, avoiding the concentration of votes on one or a few candidates.<ref>{{cite web |title='Legislative Council Election Exit Poll Analysis Article Series' No. 2 |url=http://hkupop.hku.hk/english/columns/columns56.html}}</ref>{{Unreliable source?|date=February 2024}}{{Dubious|date=February 2024}} In [[2016 Hong Kong legislative election|2016 Hong Kong Legislative Election]], the practices of strategic voting were expanded by [[Benny Tai]]'s Project ThunderGo.{{Cn|date=February 2024}} The anti-establishment camp gained 29 seats, a historical record.

=== Hungary ===
In [[Hungary]], during the [[2018 Hungarian parliamentary election]], several websites, such as taktikaiszavazas.hu<ref>taktikaiszavazas.hu</ref> (meaning "strategic voting"), promoted the idea to vote for opposition candidates with the highest probability of winning a given seat. About a quarter of opposition voters adopted this behavior, resulting in a total of 498,000 extra votes gained by opposition parties. A total of 14 extra single seats were taken by several parties and independent candidates.

=== Lithuania ===
In [[Lithuania]], which has a [[parallel voting]] system at parliamentary and district levels, most of strategic voting takes place in single-member constituencies (or districts in mayoral elections). These constituencies have two-round system when no candidate wins more than 50 per cent of the votes in the first round. A notable example of strategic voting at the parliamentary level could be the 10th [[Naujoji Vilnia]] constituency in [[2016 Lithuanian parliamentary election]]. To prevent independent candidate [[Algirdas Paleckis]]' victory, the [[Liberal Movement (Lithuania)|Liberal Movement's]], the [[Lithuanian Farmers and Greens Union]]'s and the [[Social Democratic Party of Lithuania|Social Democratic Party]]'s candidates endorsed their supporters to vote for the [[Homeland Union]]'s candidate [[Monika Navickienė]] (who came in second place). Monika Navickienė eventually won the constituency by around 900 votes.<ref>{{Cite web |title=Frontas prieš A.Paleckį Naujojoje Vilnioje: Konservatorę M.Navickienę remia net ideologiniai priešai |url=https://www.15min.lt/naujiena/aktualu/lietuva/frontas-pries-a-palecki-naujojoje-vilnioje-konservatore-m-navickiene-remia-net-ideologiniai-priesai-56-696257}}</ref><ref>{{Cite web |title=2016 m. Seimo rinkimų rezultatai – VRK.lt |url=https://www.vrk.lt/2016-seimo/rezultatai?srcUrl=/rinkimai/102/2/1306/rezultatai/lt/rezultataiVienmRpg_rpgId-18960.html}}</ref> At a district level, an example could be Kėdainiai district's mayoral election in the 2015 municipal elections. In the first round, the [[Labour Party (Lithuania)|Labour Party]] won 13 seats of 26 seats in district council and was just one seat short of absolute majority. Nijolė Naujokienė (candidate to the district's mayoral seat from the Labour Party) came short by 0.68 per cent in the mayoral election. Her opponent, Saulius Grinkevičius, had a 22 per cent gap to overcome.<ref>{{Cite web |title=Balsavimo rezultatai |url=https://www.vrk.lt/statiniai/puslapiai/2015_savivaldybiu_tarybu_rinkimai/output_lt/rezultatai_daugiamand_apygardose/apygardos_rezultatai7779.html}}</ref><ref>{{Cite web |title=Kėdainiai baigia atsikvošėti nuo Viktoro Uspaskicho kerų? |url=https://www.15min.lt/rinkimai/naujiena/savivaldybiu-tarybu-rinkimai/kedainiai-atsikvosi-nuo-viktoro-uspaskicho-keru-847-490454}}</ref> In the second round, Saulius Grinkevičius won by around 8 per cent (and 1,600 votes).<ref>{{Cite web |title=Sensacija: Darbo partija prarado Kėdainius |url=https://www.delfi.lt/news/daily/lithuania/sensacija-darbo-partija-prarado-kedainius.d?id=67435534}}</ref>

=== New Zealand ===
Since New Zealand moved to [[mixed-member proportional representation]] voting in 1996, the [[electoral system of New Zealand]] has seen strategic voting<ref>{{cite news |last1=Smith |first1=Phil |date=28 August 2017 |title=Give your vote more oomph- Strategic voting |url=https://www.rnz.co.nz/programmes/election17-backgrounders/story/201856361/election17-give-your-vote-more-oomph-strategic-voting-101 |publisher=[[RNZ]] }}</ref> regularly occur in several elections, including one party explicitly or implicitly encouraging voters to vote for a candidate other than theirs. This happened first in 1996 in the [[Wellington Central (New Zealand electorate)|Wellington Central]], and then in 1999 in the [[Coromandel (New Zealand electorate)|Coromandel]]. From 1996 until 2005, it was a regular feature in the [[Ohariu-Belmont (New Zealand electorate)|Ohariu-Belmont]] electorate,<ref>{{Cite web |date=2023-11-08 |title=Increase in split votes, election figures show |url=https://www.nzherald.co.nz/nz/increase-in-split-votes-election-figures-show/BWLL6BR2OJNFH5NN2GY5Q4SD7E/ |access-date=2023-11-08 |website=NZ Herald |language=en-NZ}}</ref> which was won by [[Peter Dunne]] throughout its existence and from 2005 in the [[Epsom (New Zealand electorate)|Epsom]] electorate which has been won solely by the [[ACT New Zealand|ACT]] party since 2005.<ref>{{Cite web |date=2023-11-08 |title=Labour gets tactical with Epsom |url=https://www.nzherald.co.nz/nz/labour-gets-tactical-with-epsom/QMFTACJYUW7SXU6ULP6EHUPUYY/ |access-date=2023-11-08 |website=NZ Herald |language=en-NZ}}</ref>

=== Poland ===
In the [[2023 Polish parliamentary election]], websites like pogonimypis.pl<ref>{{cite web |date=14 October 2023 |title=Pogonimy PiS! |url=http://pogonimypis.pl |access-date=16 October 2023 |website=pogonimypis.pl |language=pl}}</ref> (meaning "We'll chase the PiS") gave information for which voters should vote for in their constituency in order to maximize the chance of the opposition winning the extra seat. The campaign was a success, with [[Law and Justice (Poland)|PiS]] losing the majority in the [[Sejm]]. At the same time, a [[2023 Polish referendum|referendum]] with the questions asked in a persuasive way took place, with the oppositing recommending to not take the referendal card.<ref>{{cite news |last1=Przyborska |first1=Katarzyna |date=12 October 2023 |title=Co zrobić z kartą do referendum? Najlepiej nie brać |url=https://krytykapolityczna.pl/kraj/wybory-2023-co-zrobic-z-karta-do-referendum/ |work=KrytykaPolityczna.pl |language=pl-PL}}</ref> The voter turnout of the referendum is 40%, making it non-binding and merely a suggestion for all the future governments.<ref>{{cite news |last1=Tilles |first1=Daniel |date=15 October 2023 |title=Exit poll: Polish government's referendum invalidated by low turnout |url=https://notesfrompoland.com/2023/10/15/exit-poll-polish-governments-referendum-invalidated-by-low-turnout/ |work=Notes From Poland |language=en}}</ref>

=== Slovenia ===
According to some media, in the [[2011 Slovenian parliamentary election]], 30% of voters voted tactically. Public polls predicted an easy win for [[Janez Janša]], the candidate of the [[Slovenian Democratic Party]]; however, his opponent [[Zoran Janković (politician)|Zoran Janković]], the candidate of [[Positive Slovenia]], won. Prominent Slovenian public opinion researchers claimed that such proportions of strategic voting had not been recorded anywhere else before.<ref>{{cite web |date=12 December 2011 |title=Raziskovalci o anketah: zmagalo taktično glasovanje |trans-title=Researchers on the Polls: Tactical Voting Won |url=http://www.times.si/slovenija/raziskovalci-o-anketah-zmagalo-takticno-glasovanje--eba9dab4dd-6810500f55.html |url-status=dead |archive-url=https://web.archive.org/web/20120425082526/http://www.times.si/slovenija/raziskovalci-o-anketah-zmagalo-takticno-glasovanje--eba9dab4dd-6810500f55.html |archive-date=25 April 2012 |publisher=Delo.si |language=sl}}</ref>

=== Spain ===
In the 2016 General Election in Spain, the incentives for voting tactically were much larger than usual, following the rise of the Podemos and Ciudadanos and following the economic crisis and election in 2015.<ref>Stephenson, Laura B., et al., editors. ''The Many Faces of Strategic Voting: Tactical Behavior in Electoral Systems Around the World''. University of Michigan Press, {{jstor|j.ctvh4zhzr}}</ref> The strategic voters successfully influenced the outcome of the election, despite a record low turnout of 66.5%. In a natural experiment in Andalusia 9% voted strategically when having opportunity, strategic behavior did not increase with time, and did not affect surrounding electoral areas, under the assumption that strategic voting happens only for [[district magnitude]] above 5.<ref>{{cite journal |last1=Lago |first1=Ignacio |year=2012 |title=Strategic voting in proportional representation systems |url=https://doi.org/10.1177/1354068810389638 |journal=Party Politics |volume=18 |issue=5 |pages=653–665 |doi=10.1177/1354068810389638 |s2cid=143798201 |hdl-access=free |hdl=10230/48115}}</ref>

=== Taiwan ===
In the [[1995 Taiwanese legislative election|1995 Legislative Yuan election]], strategic voting was implemented by the opposition parties, such as the [[Democratic Progressive Party]]<ref name="立委選舉中民進黨的「聯合競選策略」： 以北高兩市為例2">{{cite journal |author1=林長志 |title=立委選舉中民進黨的「聯合競選策略」： 以北高兩市為例 |journal=台灣政治學刊 |language=zh |volume=13 |issue=1 |pages=58–60}}</ref> and the [[New Party (Taiwan)|New Party]].<ref>{{cite web |author1=TVBS |date=2018-08-15 |title=民進黨「懷柔喊話」配票算計高嘉瑜！憂姚文智帶衰議員選舉也垮？少康戰情室 20180815 |url=https://www.youtube.com/watch?v=L9SGBy9DuYE&t=3s |archive-url=https://web.archive.org/web/20190614065747/https://www.youtube.com/watch?v=L9SGBy9DuYE&t=3s |archive-date=2019-06-14 |access-date=2018-08-15 |website=[[YouTube]] |language=zh}}</ref> As the members were elected in multi-member districts, the parties urged their supporters to vote for a party-nominated candidate according to criteria, such as the last digit of the voter's [[National identification card (Taiwan)|National Identification Card Number]] or the voter's birth month. This maximized the opposition's seat gains and resulted in the ruling [[Kuomintang]] losing 10 seats, receiving the lowest share of seats in history at the time.

=== United Kingdom ===<!--In the [[1997 United Kingdom general election]] in [[Winchester]], [[Mark Oaten]] ([[Liberal Democrats|Liberal Democrat]]) beat the incumbent [[Conservative Party (UK)|Conservative]] MP [[Gerry Malone]] with a majority of 2 votes. Malone successfully challenged the election in the High Court, which declared it void. A [[1997 Winchester by-election|by-election]] was held which returned [[Mark Oaten]] as MP, this time with a larger majority of 21,556. This was due to the majority of Labour voters voting Liberal in the by-election.-->
In the [[1997 United Kingdom general election|1997 UK general election]], [[Democratic Left (United Kingdom)|Democratic Left]] helped [[Bruce Kent]] set up GROT (Get Rid Of Them) a strategic voter campaign whose aim was to help prevent the Conservative Party from gaining a 5th term in office. This coalition was drawn from individuals in all the main opposition parties, and many who were not aligned with any party. While it is hard to prove that GROT swung the election itself, it did attract significant media attention and brought strategic voting into the mainstream for the first time in UK politics. In 2001, the Democratic Left's successor organisation, the [[New Politics Network]], organised a similar campaign. Since then strategic voting has become a consideration in British politics as is reflected in by-elections and by the growth in sites such as tacticalvote.co.uk, who encourage strategic voting as a way of defusing the two party system and empowering the individual voter. For the [[2015 United Kingdom general election|2015 UK general election]], voteswap.org attempted to prevent the Conservative Party staying in government by encouraging Green Party supporters to tactically vote for the Labour Party in listed marginal seats. In 2017 swapmyvote.uk was formed to help supporters of all parties swap their votes with people in other constituencies.

In the 2006 local elections in London, strategic voting was promoted by sites such as London Strategic Voter in a response to national and international issues.{{fact|date=June 2024}}

In Northern Ireland, it is believed that (predominantly Protestant) Unionist voters in Nationalist strongholds have voted for the [[Social Democratic and Labour Party]] (SDLP) to prevent [[Sinn Féin]] from capturing such seats. This conclusion was reached by comparing results to the demographics of constituencies and polling districts.{{fact|date=June 2024}}

In the [[2017 United Kingdom general election|2017 general election]], it is estimated that 6.5 million people (more than 20% of voters) voted tactically<ref name="sky.com2">{{cite web |title=General Election 2017: 6.5 million voted tactically on 8 June |url=https://news.sky.com/story/general-election-2017-65-million-voted-tactically-on-8-june-10998890 |access-date=5 April 2018 |website=sky.com}}</ref> either as a way of preventing a "hard Brexit" or preventing another Conservative government led by the Tactical2017 campaign.<ref name="sky.com2" /> Many Green Party candidates withdrew from the race in order to help the Labour Party<ref>{{cite web |date=25 April 2017 |title=Green Party pulls out of crucial general election seat to help Labour beat the Tories |url=https://www.independent.co.uk/news/uk/politics/green-party-pulls-general-election-seat-ealing-help-labour-beat-tories-rupa-huq-a7701081.html |url-access=subscription |url-status=live |archive-url=https://ghostarchive.org/archive/20220526/https://www.independent.co.uk/news/uk/politics/green-party-pulls-general-election-seat-ealing-help-labour-beat-tories-rupa-huq-a7701081.html |archive-date=26 May 2022 |access-date=5 April 2018 |website=independent.co.uk}}</ref> secure closely fought seats against the Conservatives. This ultimately led to the Conservatives losing seats in the election even though they increased their overall vote share.<ref>{{Cite web |last1=Cartwright |first1=James |last2=Smith |first2=Lilly |date=6 May 2018 |title=Flipping the Script |url=https://designobserver.com/feature/flipping-the-script/39852 |work=Design Observer}}</ref>

In the [[2019 Conservative Party leadership election]] to determine the final two candidates for the party vote, it was suggested that front-runner Boris Johnson's campaign encouraged some of its MPs to back [[Jeremy Hunt]] instead of Johnson, so that Hunt{{snd}}seen as "a lower-energy challenger"{{snd}}would finish in second place, allowing an easier defeat in the party vote.<ref>{{cite web |date=20 June 2019 |title=Did Boris's dirty tricks help Hunt over Gove? |url=https://blogs.spectator.co.uk/2019/06/jeremy-hunt-and-boris-johnson-through-to-the-final-two/ |access-date=12 December 2019 |website=Coffee House}}</ref> Strategic voting was expected to play a major role in the [[2019 United Kingdom general election|2019 General Election]], with a [[YouGov]] poll suggesting that 19% of voters would be doing so tactically. 49% of strategic voters said they would do so in the hope of stopping a party whose views they opposed.<ref>{{cite news |title=Who's tactically voting, and why? {{!}} YouGov |url=https://yougov.co.uk/topics/politics/articles-reports/2019/12/10/whos-tactically-voting-and-why |access-date=12 December 2019 |work=yougov.co.uk |language=en-gb}}</ref>

According to a 2020 study, older voters in the UK vote strategically more than younger voters, and richer voters vote more strategically than poorer voters.<ref>{{Cite journal |last1=Eggers |first1=Andrew C. |last2=Vivyan |first2=Nick |date=2020 |title=Who Votes More Strategically? |journal=American Political Science Review |language=en |volume=114 |issue=2 |pages=470–485 |doi=10.1017/S0003055419000820 |issn=0003-0554 |s2cid=210896040 |doi-access=free}}</ref>

In an example of individuals voting tactically, [[Labour Party (UK)|Labour]] voters in the [[2022 Tiverton and Honiton by-election]] in the UK tactically supported the [[Liberal Democrats (UK)|Liberal Democrat]] candidate in order to ensure the defeat of the [[Conservative Party (UK)|Conservatives]].<ref>{{Cite news |last=Cecil |first=Nicholas |date=24 June 2022 |title=Sir John Curtice: Tories in trouble but Keir Starmer still missing crucial spark |url=https://www.standard.co.uk/news/politics/sir-john-curtice-analysis-by-election-results-wakefield-tiverton-honiton-keir-starmer-labour-boris-johnson-b1008172.html |url-status=live |archive-url=https://web.archive.org/web/20220624122332/https://www.standard.co.uk/news/politics/sir-john-curtice-analysis-by-election-results-wakefield-tiverton-honiton-keir-starmer-labour-boris-johnson-b1008172.html |archive-date=24 June 2022 |access-date=24 June 2022 |work=[[Evening Standard]] |quote=Sir John Curtice, Professor of Politics at Strathclyde University, [...] highlighted how many Labour voters switched to the Liberal Democrats in the Tiverton and Honiton by-election, to topple a Tory majority of 24,000. [...] 'Labour and Liberal Democrat voters are ganging up against the Tories, voting tactically,' he said.}}</ref> This resulted in the Liberal Democrats winning what had previously been a Conservative [[safe seat]].

In 2024, tactical voting was again advocated for the [[2024 United Kingdom general election|2024 general election]], as a means to defeat Conservative candidates in seats with traditional large Conservative majorities.<ref>{{Cite news |last=Walker |first=Peter |date=2024-06-17 |title=Tactical voting could defeat Tories in once safe seats, campaigners say |url=https://www.theguardian.com/politics/article/2024/jun/17/tactical-voting-guide-tories-once-safe-seats |access-date=2024-06-17 |work=The Guardian |language=en-GB |issn=0261-3077}}</ref>{{Update inline|date=August 2024}}

=== United States ===
Strategic voting in the US's [[first-past-the-post voting]] and [[presidential system]] contributes to a two-party system, where the observed effect of [[Duverger's law]] is stronger than in most countries.<ref name="Duverger2" />

In 2000, 2016, and 2024, a significant number of voters in the Presidential elections opted to use [[vote swapping]] to increase Democratic turnout in swing states and third-party turnout in safe states.<ref name=Schneider2024>{{Cite news |last=Schneider |first=Aliya |date=2024-11-03 |title=Not sold on Harris over Gaza yet anti-Trump, some Pa. activists are asking blue-state voters to cast protest ballots on their behalf |newspaper=[[The Philadelphia Inquirer]] |url=https://www.inquirer.com/politics/election/vote-swapping-pro-palestinian-protest-harris-trump-20241103.html}}</ref>

One high-profile example of strategic voting was the [[2002 California gubernatorial election]]. During the Republican primaries, Republicans [[Richard Riordan]] (former mayor of [[Los Angeles]]) and [[Bill Simon (politician)|Bill Simon]] (a self-financed businessman) vied for a chance to compete against the unpopular incumbent Democratic [[Governor of California]], [[Gray Davis]]. Polls predicted that Riordan would defeat Davis, while Simon would not. At that time, the Republican primaries were partially closed primaries in which non-partisans and registered Republicans<ref>{{Cite web |title=Voting in a Primary Election |url=https://cavotes.org/voting-in-primary-election/ |access-date=2024-11-28 |website=League of Women Voters of California {{!}} Education Fund |language=en-US}}</ref> could vote regardless of their party affiliation. Davis supporters (those were eligible to vote in the Republican primary) were rumored to have voted for Simon because Riordan was perceived as a greater threat to Davis; this, combined with a negative advertising campaign by Davis describing Riordan as a "big-city liberal", allowed Simon to win the primary despite a last-minute business [[scandal]]. The strategy to nominate Simon (if in fact it was a reality), was successful, as he lost in the general election against Davis. However, it resulted in the lowest gubernatorial general election turnout in modern California political history, thus requiring fewer signatures to qualify a [[2003 California gubernatorial recall election|recall that ultimately ousted Davis]].

Similarly, in 2012, [[Claire McCaskill]] boosted [[Todd Akin]] in the [[2012 United States Senate election in Missouri|2012 US Senate election in Missouri]]. In addition to running ads highlighting Akin's conservative stances, McCaskill also directed messages to surrogates to tell Akin to run ads which would increase his primary polling.<ref>{{Cite web |last=Mccaskill |first=Sen Claire |date=2015-08-11 |title=How I Helped Todd Akin Win –  So I Could Beat Him Later |url=http://politi.co/2Dz1clW |access-date=2024-02-03 |website=Politico Magazine |language=en}}</ref>

==== Puerto Rico ====
[[Puerto Rico]]'s 2004 elections were affected by strategic voting. Pedro Rosselló, the [[New Progressive Party of Puerto Rico|New Progressive Party]]'s candidate of that year, was unpopular across much of the territory due to large corruption schemes and the privatization of public corporations. To prevent Rossell from winning, other factions supported the [[Popular Democratic Party (Puerto Rico)|Partido Popular Democratico]]'s candidate. The elections were close; statehood advocates won a seat in the U.S. house of representatives and majorities in both legislative branches, but lost governance to [[Aníbal Acevedo Vilá]]. (Puerto Ricans have the chance to vote by party or by candidate. Separatists voted under their ideology but for the center party's candidate, which caused major turmoil.) After a recount and a trial, Acevedo Vilá was certified as governor of the Commonwealth of Puerto Rico.

== Rational voter model ==
Analysis of strategic voting is commonly based on a model of behavior where voters are ''short-term instrumentally rational''. That is, voters are only voting in order to make an impact on one election at a time (not, say, to build the [[political party]] for next election); voters have a set of sincere preferences, or utility rankings, by which to rate candidates; voters have some knowledge of each other's preferences; and voters understand how best to use strategic voting to their advantage. The extent to which this model resembles real-life elections is the subject of considerable academic debate.

=== Myerson–Weber strategy ===
An example of a rational voter strategy is described by [[Roger Myerson|Myerson]] and Weber.<ref>{{cite journal |last1=Myerson |first1=Roger B. |last2=Weber |first2=Robert J. |year=1993 |title=A Theory of Voting Equilibria |url=http://www.kellogg.northwestern.edu/research/math/papers/782.pdf |journal=The American Political Science Review |volume=87 |issue=1 |pages=102–114 |doi=10.2307/2938959 |jstor=2938959 |s2cid=143828854 |hdl-access=free |hdl=10419/221141}}</ref> The strategy is broadly applicable to a number of single-winner voting methods that are additive point methods, such as [[Plurality voting method|Plurality]], [[Borda count|Borda]], [[Approval voting|Approval]], and [[Range voting|Range]]. The strategy is optimal in the sense that the strategy will maximize the voter's [[Utility#Expected utility|expected utility]] when the number of voters is sufficiently large.

This rational voter model assumes that the voter's utility of the election result is dependent only on which candidate wins and not on any other aspect of the election, for example showing support for a losing candidate in the vote tallies. The model also assumes the voter chooses how to vote individually and not in collaboration with other voters.

Given a set of ''k'' candidates and a voter let:

: ''v<sub>i</sub>'' = the number of points to be voted for candidate ''i''
: ''u<sub>i</sub>'' = the voter's gain in utility if candidate ''i'' wins the election
: ''p<sub>ij</sub>'' = the (voter's perceived) ''pivot probability'' that candidates ''i'' and ''j'' will be tied for the most total points to win the election.

Then the voter's ''prospective rating'' for a candidate ''i'' is defined as:

: <math>R_i = \sum_{j \neq i} \; p_{ij} \cdot (u_i - u_j)\,</math>

The gain in expected utility for a given vote is given by:

: <math>G(p,v,u) = \sum_{i=1}^k \; v_i \cdot R_i\,</math>

The gain in expected utility can be maximized by choosing a vote with suitable values of ''v<sub>i</sub>'', depending on the voting method and the voter's prospective ratings for each candidate. For specific voting methods, the gain can be maximized using the following rules:

* Plurality: Vote for the candidate with the highest prospective rating. This is different from choosing the best of the frontrunners, which is a common [[heuristic]] approach to voting. In rare cases, the highest prospective rating can belong to a weak candidate (one with a low probability of winning).
* Borda: Rank the candidates in decreasing order of prospective rating.
* Approval: Vote for all candidates that have a positive prospective rating.
* Range: Vote the maximum (minimum) for all candidates with a positive (negative) prospective rating.

Pivot probabilities are rarely estimated in [[political forecasting]], but can be estimated from predicted winning probabilities. An important special case occurs when the voter has no information about how other voters will vote. This is sometimes referred to as the ''zero information strategy''. In this special case, the ''p<sub>ij</sub>'' pivot probabilities are all equal and the rules for the specific voting methods become:

* Plurality: Vote for the most preferred (highest utility) candidate. This is the sincere plurality vote.
* Borda: Rank the candidates in decreasing order preference (decreasing order of utility). This is the sincere ranking of the candidates.
* Approval: Calculate the average utility of all candidates. Vote for all candidates that have a higher-than-average utility; do not vote for any candidates that have a lower-than-average utility.
* Range: Calculate the average utility of all candidates. Vote the maximum points for all candidates that have a higher-than-average utility; vote the minimum points for all candidates that have a lower-than-average utility; vote any value for a candidate with a utility equal to the average.

Myerson and Weber also describe voting equilibria that require all voters use the optimal strategy and all voters share a common set of ''p<sub>ij</sub>'' pivot probabilities. Because of these additional requirements, such equilibria may in practice be less widely applicable than the strategies.

== Pre-election influence ==
Strategic voting requires voters to be informed, as they can only gauge who is in the leading and who may not be a viable candidate through the information they are supplied.<ref>{{Cite book |last1=Aldrich |first1=John |url=https://www.fulcrum.org/concern/monographs/c534fp904 |title=The Many Faces of Strategic Voting: Tactical Behavior in Electoral Systems Around the World |last2=Blais |first2=André |last3=Stephenson |first3=Laura |date=2018 |publisher=University of Michigan Press |isbn=978-0-472-13102-0 |location=Ann Arbor|page=106 |language=en |doi=10.3998/mpub.9946117}}</ref> Because strategic voting relies heavily on voters' perception of how other voters intend to vote, campaigns in electoral methods that promote compromise frequently focus on affecting voters' perception of campaign viability. Most campaigns craft refined media strategies to shape the way voters see their candidacy. During this phase, there can be an analogous effect where campaign donors and activists may decide whether or not to support candidates tactically with their money and time.

In [[Rolling election|rolling elections]], where some voters have information about previous voters' preferences (e.g. presidential [[Partisan primary|primaries]] in the United States), candidates put disproportionate resources into competing strongly in the first few stages, because those stages affect the reaction of later stages.

Perceived influence on other voters also interacts with strategic voting. In a study of the Israeli voting system, presumed media influence was found to be a variable in the case of why voters partake in strategic voting.<ref>{{Cite journal |last1=Cohen |first1=Jonathan |last2=Tsfati |first2=Yariv |date=2009-06-01 |title=The Influence of Presumed Media Influence on Strategic Voting |url=https://journals.sagepub.com/doi/10.1177/0093650209333026 |journal=Communication Research |language=en |volume=36 |issue=3 |pages=359–378 |doi=10.1177/0093650209333026 |issn=0093-6502}}</ref> Because the Israeli electoral system is complex, with many parties, and parliamentary, this perceived media influence effect may have a larger and more observable effect on simpler systems such as the one in the United States. 

[[Game theory]] has been used to search for some kind of "minimally manipulable" ([[incentive compatibility]]) voting schemes. Game theory can also be used to analyze the pros and cons of different methods. For instance, when electors vote for their own preferences rather than tactically, [[Condorcet method]]-like methods tend to settle on compromise candidates, while [[instant-runoff voting]] favors those candidates with strong core support but otherwise narrower appeal due to holding more uncompromising positions. Thus, [[Condorcet methods]] incentivize candidates to position themselves closer to the [[median voter]] and appeal to a wider section of the electorate than [[instant-runoff voting]] does.<ref name="k899">{{cite journal | last=Robinette | first=Robbie | title=Implications of strategic position choices by candidates | journal=[[Constitutional Political Economy]] | volume=34 | issue=3 | date=2023 | issn=1043-4062 | doi=10.1007/s10602-022-09378-6 | doi-access=free | pages=445–457}}</ref><ref name="r517">{{cite journal | last=Ogren | first=Marcus | title=Candidate incentive distributions: How voting methods shape electoral incentives | journal=[[Electoral Studies]] | publisher=Elsevier BV | volume=90 | year=2024 | issn=0261-3794 | doi=10.1016/j.electstud.2024.102799 | arxiv=2306.07147 | page=102799}}</ref>{{rp|Fig 4.1}}

== By method ==

=== Plurality voting ===
{{See also|Plurality voting#Tactical voting}}
Lesser-evil voting is exceedingly common in [[Plurality voting method|plurality]] elections, where the first preference is all that counts (and thus lesser-evil voting is the only effective kind of strategic voting). The most typical tactic is to assess which two candidates are frontrunners (most likely to win) and to vote for the preferred one of those two, even if a third candidate is preferred over both. [[Duverger's law]] is the observation that this kind of strategic voting and [[strategic nomination]] is sufficiently common for any method based on first preferences to produce two-party domination.

=== Plurality-runoff family (RCV, two-round, and partisan primaries) ===
{{See also|Instant-runoff voting#Resistance to tactical voting}}
Theoretical results indicate that, under two-round runoff voting with three candidates, strategic equilibria exist in which only two candidates receive votes.<ref>{{Cite journal |last=Bouton |first=Laurent |date=2013 |title=A Theory of Strategic Voting in Runoff Elections |url=https://www.jstor.org/stable/23469618 |journal=The American Economic Review |volume=103 |issue=4 |pages=1248–1288 |doi=10.1257/aer.103.4.1248 |issn=0002-8282 |jstor=23469618}}</ref> It has been shown experimentally that voters are influenced by a candidate's perceived likelihood of winning the election.<ref>{{Cite journal |last1=Blais |first1=André |last2=Labbé-St-Vincent |first2=Simon |last3=Laslier |first3=Jean-François |last4=Sauger |first4=Nicolas |last5=Van der Straeten |first5=Karine |date=2011 |title=Strategic Vote Choice in One-round and Two-round Elections: An Experimental Study |url=https://www.jstor.org/stable/23056381 |journal=Political Research Quarterly |volume=64 |issue=3 |pages=637–645 |doi=10.1177/1065912909358583 |issn=1065-9129 |jstor=23056381 |s2cid=14130949}}</ref>

[[Instant-runoff voting|Instant runoff voting]] is vulnerable to three of the four kinds of strategy discussed above. It is vulnerable to lesser-evil voting; to turkey-raising; and to strategic truncation.

There is a common misconception that instant-runoff is not affected by a kind of strategic voting called [[Truncation (voting)|truncation]] or [[bullet voting]].<ref>{{cite web |last1=The Non-majority Rule Desk |date=July 29, 2011 |title=Why Approval Voting is Unworkable in Contested Elections - FairVote |url=http://www.fairvote.org/why-approval-voting-is-unworkable-in-contested-elections |accessdate=11 October 2016 |website=FairVote Blog}}</ref> However, satisfying later-no-harm does not (by itself) provide resistance to such strategies, unless paired with the [[participation criterion]]. Systems like [[Instant runoff voting|instant runoff]] that pass later-no-harm but fail [[Participation criterion|participation]] still incentivize truncation or bullet voting in some situations.<ref name=":12" /><ref>{{Cite journal |last1=Graham-Squire |first1=Adam |last2=McCune |first2=David |date=2023-06-12 |title=An Examination of Ranked-Choice Voting in the United States, 2004–2022 |url=https://www.tandfonline.com/doi/full/10.1080/00344893.2023.2221689 |journal=Representation |language=en |pages=1–19 |arxiv=2301.12075 |doi=10.1080/00344893.2023.2221689 |issn=0034-4893}}</ref>

=== Cardinal single-winner voting ===
{{See also|Score voting#Strategy|Approval voting#Strategy}}
Most cardinal, single-winner voting systems in large elections encourage similar strategies:

# Calculate the expected (average) utility of the election result (the average [[utility]] if the election was repeated many times).
# Top-rate all candidates with above-average utility, and bottom-rate all candidates with below-average utility.

Such a strategy involves "semi-honest exaggeration". Unlike in most voting systems, voters rarely (if ever) have an incentive to lie about which of two candidates they prefer, which makes such far milder than under other voting systems. Voters exaggerate the difference between a certain pair of candidates but do not rank any less-preferred candidate over any more-preferred one. This form of exaggeration has an effect whenever the voter's honest rating for the intended winner is below that candidate's median rating; or when their honest rating for the intended loser is above it. In other words, half of voters will have an incentive to strategize, while half will not.

Typically, this would not be the case unless there were two similar candidates favored by the same set of voters. A strategic vote against a similar rival could result in a favored candidate winning; although if voters for both similar rivals used this strategy, it could cause a candidate favored by neither of these voter groups to win.

[[Michel Balinski|Balinski]] and Laraki noted that under majority judgment, many voters have no opportunity or incentive to use strategy. They argued based on a simulation that the highest median methods minimized the number of voters with an incentive to misrepresent their opinions, among the methods they studied.<ref name=mjrank>{{cite book | last1=Balinski | first1=M. L. | last2=Laraki | first2=Rida | title=Majority judgment: measuring, ranking, and electing  | publisher=MIT Press | publication-place=Cambridge, Mass. | date=2010 | isbn=978-0-262-01513-4}}{{page?|date=February 2025}}</ref>

Strategic voters are faced with the initial tactic as to how highly to score their second-choice candidate. The voter may want to retain expression of a high preference of their favorite candidate over their second choice. But that does not allow the same voter to express a high preference of their second choice over any others.

In [[approval voting]], because the only option is to approve of a candidate or not, optimal strategic voting rarely includes ranking a less-preferred candidate over a more-preferred candidate. However, strategy is in fact inevitable when a voter decides their "approval cutoff". [[Steven Brams]] and [[Dudley R. Herschbach]] argued in a paper in ''[[Science (journal)|Science]]'' magazine in 2001 that [[approval voting]] was the method least amenable to tactical perturbations.<ref name="Heschbach2">{{cite journal |last1=Hershbach |first1=Dudley |last2=Brams |first2=Steven |date=2001-05-25 |title=The Science of Elections |url=https://www.science.org/doi/full/10.1126/science.292.5521.1449 |journal=Science |volume=292 |issue=5521 |page=1449 |doi=10.1126/science.292.5521.1449 |pmid=11379606 |access-date=2024-05-10}}</ref>

Balinski and Laraki used rated ballots from a poll of the [[2007 French presidential election]] to show that, if unstrategic voters only approved candidates whom they considered "very good" or better, strategic voters would be able to sway the result frequently, but that if unstrategic voters approved all candidates they considered "good" or better, approval was the second most strategy-resistant method of the ones they studied, after majority judgment itself.<ref name="mjrank" />

=== Ranked single-winner voting ===
{{See also|Borda count#Potential for tactical manipulation}}
The [[Borda count]] has both a strong incentive and a large vulnerability to burial. Here is a hypothetical example of both factors at the same time: if there are two candidates the most likely to win, the voter can maximize the impact on the contest between these candidates by ranking the candidate the voter likes more in first place, ranking the candidate whom they like less in last place. If neither candidate is the sincere first or last choice, the voter is using both the compromising and burying strategies at once. If many different groups voters use this strategy, this gives a paradoxical advantage to the candidate generally thought least likely to win.{{Cn|date=May 2024}}

=== Condorcet ===
{{See also|Condorcet method#Potential for tactical voting}}
[[Condorcet method|Condorcet methods]] are vulnerable to 3 of the 4 kinds of strategy listed above, because the [[Condorcet winner criterion]] is incompatible with the [[sincere favorite criterion]], [[participation criterion]], [[later-no-harm]], and [[later-no-help]]. Strategy in Condorcet methods can become highly complex, but almost always involves burial or truncation.

=== Multi-winner voting ===
==== Single transferable vote ====
{{See also|Single transferable vote#Tactics}}
The [[single transferable vote]] may incentivize free-riding: if a voter expects their favorite candidate will almost-certainly be elected, insincerely ranking the second candidate first does not hurt the favored candidate.<ref>{{cite web |last=Schulze |first=Markus |title=Free Riding and Vote Management under Proportional Representation by the Single Transferable Vote |url=http://m-schulze.9mail.de/schulze2.pdf |access-date=2016-03-14}}</ref>

Some forms of STV allow strategic voters to gain an advantage by listing a candidate who is very likely to lose in first place.<ref>{{cite web |last=Woodall |first=Douglas R. |date=March 1994 |title=Computer counting in STV elections |url=http://www.votingmatters.org.uk/ISSUE1/P3.HTM |access-date=6 March 2011 |publisher=McDougall Trust}}</ref> This strategy, called ''Woodall free riding'', is essentially eliminated by [[Counting single transferable votes#Meek|Meek's method]]; however, Meek's method is rarely used because of its substantial complexity, having been adopted only for some local elections in New Zealand.<ref>{{cite journal |author=Markus Schulze |date=June 2004 |title=Free Riding |url=http://www.votingmatters.org.uk/ISSUE18/I18P2.PDF |journal=Voting Matters |issue=18 |pages=2–8}}</ref>

In Malta's STV, the two-party system can cause strategic voting away from third parties.{{Cn|date=May 2024}}

== See also ==
{{Portal|Politics}}

* [[Electoral fusion]]
* [[Keynesian beauty contest]]
* [[Lesser of two evils]]
* [[Partisan primary|Primary election]]
* [[Ranked voting]]
* [[Strategic nomination]]
* [[Vote allocation]]
* [[Vote swapping]]

== References ==
<references responsive="0"></references>

== Sources ==

* {{cite book |last=Cox |first=Gary |url=http://productsearch.barnesandnoble.com/search/results.aspx?store=BOOK&WRD=gary+cox+%22making+votes+count%22&box=gary%20cox%20%22making%20votes%20count%22 |title=Making Votes Count : Strategic Coordination in the World's Electoral Systems |publisher=[[Cambridge University Press]] |year=1997 |isbn=978-0-521-58527-9 |page=340 |archive-url=https://web.archive.org/web/20150625023804/http://productsearch.barnesandnoble.com/search/results.aspx?store=book |archive-date=25 June 2015 |url-status=dead}}
* Svensson, Lars-Gunnar (1999). [http://swopec.hhs.se/lunewp/abs/lunewp1999_001.htm "The Proof of the Gibbard–Satterthwaite Theorem Revisited"]
* Fisher, Stephen (2001). "Extending the Rational Voter Theory of Tactical Voting" {{ISBN?}}

== External links ==

* [https://web.archive.org/web/20060428044816/http://emptymoat.blogspot.com/2004/07/tactical-voting-can-be-weak-strategy.html Tactical Voting Can Be a Weak Strategy]{{snd}}Article on strategic voting within larger strategic considerations [archived]
* {{Cite web |date=20 October 2004 |title=FAQs |url=http://www.votepair.org/faq.php |url-status=dead |archive-url=https://web.archive.org/web/20080917080622/http://www.votepair.org/faq.php |archive-date=17 September 2008 |website=VotePair: Uniting Progressives Through Strategic Voting}}
* [http://www.voteroll.com/ VoteRoll.com] VoteRoll is a blog roll voting system that offers tiered strategic voting to develop statistics for people voting online since 2010.


{{DEFAULTSORT:Strategic Voting}}
[[Category:Voting theory]]
[[Category:Psephology]]
[[Category:Party-list proportional representation]]